ITR Atlas
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BrainGate Radial Keyboard (Bacher et al., 2015)

Measured by Bacher, Jarosiewicz, Masse, Stavisky, Simeral, Hochberg et al. · Neurorehabil. Neural Repair 29(5) (2015)

Intracortical Keyboard invasive 2015

Inputs

The measured or assumed values behind the calculations, each with its source.

rate = 10.4 correct char/min
Best reported Radial Keyboard copy-spelling condition: 10.4 +/- 2.4 correct characters/min in the 'quick fox' task.
H = 1.0 bits/char
English-text entropy (Shannon); the task was error-free copy spelling via a virtual keyboard.
accuracy = 91.4 %
Radial Keyboard accuracy in the 'quick fox' task was 91.4 +/- 5.8% correct; errors had to be corrected to complete the task.
N = 28
Keys on the Radial Keyboard layout, for the raw-key Wolpaw bound (uniform prior over the alphabet). The headline Shannon figure uses English entropy instead.
T_key = 5.27 s/key
Gross key-selection interval for the Wolpaw bound: 60 / (10.4 correct cpm / 0.914 accuracy) = 5.27 s. Gross (errors included) because Wolpaw's accuracy term P handles them separately.

Strictest ITR

Each scoring method is an upper bound on the channel, so the headline is the strictest (smallest) one for this entry. Use the score selector on the home page to view any single method across entries.

Strictest Shannon (text) Recomputed
Character-entropy throughput (realized text entry)
Net of English redundancy
0.173 bits/s

  1. Correct characters per minute

    10.4 correct char/min

    Bacher et al. report 10.4 +/- 2.4 ccpm for the Radial Keyboard in the 'quick fox' copy-spelling task. The participant had to correct errors to complete the prompted text.

  2. Bits per character

    H(English) ~= 1.0 bit/char

  3. Information transfer rate

    10.4 char/min × 1.0 bit/char ÷ 60 s/min = 0.173 bits/s

What counts as a bit depends on the action space. The number of distinguishable actions and how likely each one is are design choices of the task, not the sensing hardware. The same modality can present a fixed set of targets, a set pruned per step by a grammar or language model, or a continuous control space. Each of these changes how many actions are live and how the probability mass is spread, and therefore the information per selection. Read the action space below before comparing headline numbers across entries.

Action space

What the user can produce at each step, and how those options are distributed.

Structure
Fixed set of targets
Size
28 distinguishable actions
Prior
Context-conditioned: likelihoods depend on prior actions
Notes
An intracortical point-and-click cursor used with the BrainGate Radial Keyboard. The radial layout reduced cursor travel compared with QWERTY and enabled face-to-face text-to-speech and remote chat. Since the realized output is English text, the reference calculation follows the same character-entropy convention as the Kennedy, Synchron and BrainGate2 text-entry entries.

Comparability The strictest bound here is the Shannon entropy of the output text, under one predictor held constant across the whole atlas (≈1 bit per character). That shared predictor makes it directly comparable to every other text entry (keyboards, spellers, silent speech and speech BCIs) regardless of prior or vocabulary size. For most text interfaces it comes out tighter than the raw-selection bounds, but not always. Where a small vocabulary makes Wolpaw tighter, that wins instead. Any Fitts, Wolpaw or log₂(N) figure shown below is another bound on the same channel. Switch the home-page score selector to compare one across entries.

Other bounds considered for the headline

Also valid upper bounds for this entry and eligible to be the headline. They just came out looser than the strictest above. Pick any of these in the home-page score selector.

Wolpaw Recomputed
Wolpaw bitrate over the raw key set
Uniform-prior ceiling on the key channel, before English redundancy
0.754 bits/s

  1. Bits per selection (Wolpaw formula)

    B = log2(N) + P*log2(P) + (1-P)*log2((1-P)/(N-1))
  = log2(28) + 0.914*log2(0.914) + 0.086*log2(0.086/27)
  = 3.975 bits / selection

    Term 1 is the information if every choice were correct; terms 2-3 subtract the bits lost to the error rate, assumed spread evenly over the other N-1 targets.

  2. Selections per second

    T = 5.27 s/selection  ->  1 / 5.27 = 0.19 selections/s

  3. Information transfer rate

    ITR = B * selections/s = 3.975 * 0.19 = 0.754 bits/s

Other score types

Bounds the atlas keeps out of the default strictest headline: as-reported figures, alternate task conditions, or raw-channel ceilings that shouldn't win the headline by default. Each still carries a score type, so the home-page selector ranks this entry on it when you choose that type. Read its derivation before comparing across entries.

Nuyujukian Recomputed
Nuyujukian achieved bitrate over the raw key set
Achieved-bitrate view of the key channel, shown for comparison
0.75 bits/s

  1. Achieved-bitrate credit per net-correct key

    N = 28 keys → log2(N − 1) = log2(27) = 4.75 bits per net-correct selection (field-standard achieved bitrate, e.g. Webgrid; Nuyujukian 2015, which introduced the metric, used log2(N)).

  2. Net-correct key rate

    net-correct = 2P − 1 = 2(0.914) − 1 = 0.828 of keys. At 5.27 s/key → 0.828 / 5.27 = 0.157 correct/s.

    A keyboard error commits the wrong key rather than timing out, so incorrect = 1 − P. Same N (28 keys), accuracy (91.4%) and key interval (5.27 s) as the entry's raw-key Wolpaw ceiling; netting each wrong key against a correct one (2P − 1) lands just under the ~0.75 bits/s Wolpaw figure. Both are the uniform-prior key channel, above the 0.173 bits/s Shannon headline.

  3. Achieved bitrate

    4.75 bits × 0.157 correct/s = 0.75 bits/s.

Source

Authors
Bacher, Jarosiewicz, Masse, Stavisky, Simeral, Hochberg et al.
Publication
Neurorehabil. Neural Repair 29(5), 2015
Paper
10.1177/1545968314554624
Reference
SAGE full text
Reference
BrainGate publication videos